First create a virtual host, and go to that directory.
Install dependencies:

sudo apt-get install libapache2-mod-php5 php5-gd php5-json php5-mysql php5-curl php5-intl php5-mcrypt php5-imagick

Download and extract owncloud package (Find latest version here:

wget https://download.owncloud.org/community/owncloud-9.1.3.tar.bz2
tar xf owncloud-9.1.3.tar.bz2 && rm owncloud-9.1.3.tar.bz2
cd owncloud
mv * ../
mv .* ../

Now create a new database, a new user for that database and grant privileges for that user on that database. This can be done manually on the mysql command line or via phpmyadmin.

Go to the publicly accessible url and input these settings for a wizard install of owncloud.

If you want an ssl-only access to owncloud, first setup certificates on the server, and after verifying that the https:// url works fine, enter the following at the start of .htaccess file in the root of public web directory:

RewriteEngine On
RewriteCond %{SERVER_PORT} 80
RewriteRule ^(.*)$ https://cloud.yoursite.com/$1 [R,L]